D: The Infinite Square Roots of -1

p. 229-235

Résumé

We present D, a synbol that can be used in the universal alphabet that provides a computational path to the nilpotent Dirac equation (Diaz & Rowlands, 2004) and which results in a tractable computer representation of the infinite square roots of -1. We outline how the representation is derived, the properties of the representation, and how the form can be used. Think of D as an infinite table of 1's in any representation e.g. binary or hexadecimal. Any specified column Di of the table has the property that when multiplied with a row Di, the result is a representation of -1. Di multiplied with Dj anticommutes as - (Dj*Di) and produces Dk in a way identical to Hamilton's quaternion i, j, and k. With an infinite and uniquely identifiable set of such triad forms D can be considered both a symbol and because of this behaviour, an alphabet.

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Référence papier

Bernard M. Diaz et Peter Rowlands, « D: The Infinite Square Roots of -1 », CASYS, 19 | 2006, 229-235.

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Bernard M. Diaz et Peter Rowlands, « D: The Infinite Square Roots of -1 », CASYS [En ligne], 19 | 2006, mis en ligne le 29 August 2024, consulté le 20 September 2024. URL : http://popups.lib.uliege.be/1373-5411/index.php?id=2586

Auteurs

Bernard M. Diaz

Department of Computer Science

The University of Liverpool

Peach Street, Liverpool, UK, L69 7ZF

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Peter Rowlands

Science Communication Unit, Department of Physics

The University of Liverpool

Peach Street, Liverpool, UK, L69 7ZF

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CC BY-SA 4.0 Deed